This paper presents a new modal logic for ceteris paribus preferences understood in the sense of "all other things being equal". This reading goes back to the seminal work of Von Wright in the early 1960's and has returned in computer science in the 1990' s and in more abstract "dependency logics" today. We show how it differs from ceteris paribus as "all other things being normal", which is used in contexts with preference defeaters. We provide a semantic analysis and (...) several completeness theorems. We show how our system links up with Von Wright's work, and how it applies to game-theoretic solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary modal logics. (shrink)

This paper presents a new modal logic for ceteris paribus preferences understood in the sense of “all other things being equal”. This reading goes back to the seminal work of Von Wright in the early 1960’s and has returned in computer science in the 1990’s and in more abstract “dependency logics” today. We show how it differs from ceteris paribus as “all other things being normal”, which is used in contexts with preference defeaters. We provide a semantic analysis and several (...) completeness theorems. We show how our system links up with Von Wright’s work, and how it applies to game-theoretic solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary modal logics. (shrink)

Simple finite axiomatizations are given for versions of the modal logics K and K4 with non-contingency (or contingency) as the sole modal primitive. This answers two questions of I. L. Humberstone.

The paper attempts to give a solution to the Fitch's paradox though the strategy of the reformulation of the paradox in temporal logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism.

The formula A (it is noncontingent whether A) is true at a point in a Kripke model just in case all points accessible to that point agree on the truth-value of A. We can think of -based modal logic as a special case of what we call the general modal logic of agreement, interpreted with the aid of models supporting a ternary relation, S, say, with OA (which we write instead of A to emphasize the generalization involved) true at a (...) point w just in case for all points x, y, with Swxy, x and y agree on the truth-value of A. The noncontingency interpretation is the special case in which Swxy if and only if Rwx and Rwy, where R is a traditional binary accessibility relation. Another application, related to work of Lewis and von Kutschera, allows us to think of OA as saying that A is entirely about a certain subject matter. (shrink)

The idea of a property's being supervenient on a class of properties is familiar from much philosophical literature. We give this idea a linguistic turn by converting it into the idea of a predicate symbol's being supervenient on a set of predicate symbols relative to a (first order) theory. What this means is that according to the theory, any individuals differing in respect to whether the given predicate applies to them also differ in respect to the application of at least (...) one of the predicates in the set. The latter relationship we show turns out to coincide with something antecedently familiar from work on definability: with what is called the piecewise (or modelwise) definability, in the theory in question, of the given predicate in terms of those in the set. (shrink)

The main topic of this paper is the question of how supervenience can be understood as a relation between two families of properties each applicable to a distinct domain of individuals.

THIS PAPER CORRECTS AN ERROR IN MY EARLIER PAPER, "CONCEPTS OF SUPERVENIENCE" ("PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH", VOLUME 45, 1984), AND PRESENTS FURTHER MATERIAL ON SUPERVENIENCE. THE ERROR IS THE CLAIM THAT "GLOBAL" SUPERVENIENCE ENTAILS "STRONG" SUPERVENIENCE. HOWEVER, IT IS ARGUED THAT THIS FAILURE OF ENTAILMENT ONLY GOES TO SHOW THE INADEQUACY OF GLOBAL SUPERVENIENCE AS AN EXPLICATION OF "DEPENDENCY" OR "DETERMINATION" RELATION, AND, IN PARTICULAR, THAT MATERIALISM FORMULATED IN TERMS OF GLOBAL SUPERVENIENCE APPEARS TOO WEAK. (IT IS POINTED OUT, AMONG (...) OTHER THINGS, THAT GLOBAL SUPERVENIENCE DOES NOT ENTAIL "WEAK" SUPERVENIENCE). A STRONGER FORM OF GLOBAL SUPERVENIENCE, BASED ON "SIMILARITY" RATHER THAN "INDISCERNIBILITY" BETWEEN WORLDS, IS FORMULATED AND BRIEFLY DISCUSSED. (shrink)

We consider the modal logic of non-contingency in a general setting, without making special assumptions about the accessibility relation. The basic logic in this setting is axiomatized, and some of its extensions are discussed, with special attention to the expressive weakness of the language whose sole modal primitive is non-contingency , by comparison with the usual language based on necessity.

An analogy between functional dependencies and implicational formulas of sentential logic has been discussed in the literature. We feel that a somewhat different connexion between dependency theory and sentential logic is suggested by the similarity between Armstrong's axioms for functional dependencies and Tarski's defining conditions for consequence relations, and we pursue aspects of this other analogy here for their theoretical interest. The analogy suggests, for example, a different semantic interpretation of consequence relations: instead of thinking ofB as a consequence of (...) a set of formulas {A1,...,A n} whenB is true on every assignment of truth-values on which eachA i is true, we can think of this relation as obtaining when every pair of truth-value assignments which give the same truth-values toA 1, the same truth-values toA 2,..., and the same truth-values toA n, also make the same assignment in respect ofB. We describe the former as the consequence relation inference-determined by the class of truth-value assignments (valuations) under consideration, and the latter as the consequence relation supervenience-determined by that class of assignments. Some comparisons will be made between these two notions. (shrink)

I argue that the semantic thesis of direct reference and the meta- physical thesis of the supervenience of the non-physical on the physical cannot both be true. The argument first develops a necessary condition for supervenience, a so-called conditional locality requirement, which is then shown to be incompatible with some physical object having object dependent properties, which in turn is required for the thesis of direct reference to be true. We apply this argument to formulate a new argument against the (...) claim that a thisness is analyzable in purely general terms, one that does not rely on complete symmetry nor the falsity of the identity of indiscernibles. I outline a strategy at the end how the conclusion could be avoided, at a price. (shrink)

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L_D and L_I, based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue (...) that L_D and L_I naturally resolve a range of interpretational problems that arise in D and I.We also obtain sound and complete axiomatizations for L_D and L_I . (shrink)

The semantics for counterfactuals due to David Lewis has been challenged by appealing to miracles. Miracles may skew a given similarity order in favour of those possible worlds which exhibit them. Lewis responded with a system of priorities that mitigates the significance of miracles when constructing similarity relations. We propose a prioritised ceteris paribus analysis of counterfactuals inspired by Lewis’ system of priorities. By analysing the couterfactuals with a ceteris paribus clause one forces out, in a natural manner, those possible (...) worlds which do not satisfy the requirements of the clause, thus excluding miracles. If no world can satisfy the ceteris paribus clause in its entirety, then prioritisation is triggered to select worlds that maximise agreement on those things which are favoured most. (shrink)

A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator? but without the necessity operator 2. This logic is not a normal modal logic, because?→ is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over (...) classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap. (shrink)

Inspired by the supervenience-determined consequence relation and the semantics of agreement operator, we introduce a modal logic of supervenience, which has a dyadic operator of supervenience as a sole modality. The semantics of supervenience modality very naturally correspond to the supervenience-determined consequence relation, in a quite similar way that the strict implication corresponds to the inference-determined consequence relation. We show that this new logic is more expressive than the modal logic of agreement, by proposing a notion of bisimulation for the (...) latter. We provide a sound proof system for the new logic. We lift onto more general logics of supervenience. Related to this, we address an interesting open research direction listed in the literature, by comparing propositional logic of determinacy and noncontingency logic in expressive powers and axiomatizing propositional logic of determinacy over various classes of frames. We also obtain an alternative axiomatization for propositional logic of determinacy over universal models. (shrink)

Hilbert-style axiomatic systems are presented for versions of the modal logics K, where {D, 4, 5}, with noncontingency as the sole modal primitive. The classes of frames characterized by the axioms of these systems are shown to be first-order definable, though not equal to the classes of serial, transitive, or euclidean frames. The canonical frame of the noncontingency logic of any logic containing the seriality axiom is proved to be nonserial. It is also shown that any class of frames definable (...) in the noncontingency language contains the class of functional frames, and dually, there exists a greatest consistent normal noncontingency logic. (shrink)

The sophisticated philosophical literature on supervenience stands in need of supplementation by a treatment of more fundamental questions about what features this notion possesses solely in virtue of the form of the definition it is standardly given. We provide a discussion of these features without getting involved in the merits of particular supervenience claims advanced and contested in that literature.

Developing and motivating the notion of supervenience. Investigating the relationship to reducibility and definability (equivalence, under certain conditions), and to microphysical determination.